Rene Meulensteen’s side had taken the lead through Steve Sidwell in the 18th minute and made no apologies for their unambitious gameplan as they were pounded by the hosts.
Robin van Persie equalised for United with 12 minutes left and Michael Carrick’s deflected shot 80 seconds later looked to have sealed the comeback.
It was enough to send Moyes on to the playing surface and, while it was hardly Brian Kidd against Sheffield Wednesday, as he turned to face the South Stand he roared and pumped his fist with relief.
It could have been the start of something new but a weak header from Nemanja Vidic after three minutes of stoppage time allowed Sidwell to slide the ball through for Kieran Richardson.
The former Manchester United man’s shot was pushed into the air by David de Gea and Bent headed in from just a couple of yards as Fulham, a team that had lost 13 of their previous 16 league matches, snatched an unlikely draw.
Afterwards Moyes rolled his eyes at questions about his team sending over 81 crosses, of which only 18 found a team-mate, suggesting it was too simplistic to claim that was United’s only tactic.
Although Meuelensteen, who left his coaching job at Old Trafford in the summer despite being invited to stay on, was polite about it, there was no mistaking his view that United were predictable.
While it is never easy to break down a team that had no intention of doing anything positive, it is doing just that time and time again that makes champions.
And, having been nine points clear of Manchester City on their way to winning the title at this stage last season, United are now nine points adrift of Liverpool in fourth and have won just six of their 13 home games this season.
For all the statistics that were flying together last night, they are the only ones that really matter.
It took only a few seconds for it to become clear that Fulham were happy for United to have complete control of possession until they came within 10 yards of the visitors’ box.
But for all their territory, United had not threatened Fulham goalkeeper Maarten Stekelenburg before the visitors moved in front after 18 minutes.
John Arne Riise won the ball from Juan Mata in midfield and Lewis Holtby was given the time and space to lift the ball over the United defence for Sidwell to find the corner with a first-time volley.
As United attempted to respond, they finally created a clear chance when Rafael crossed to the far post but van Persie blasted well wide from just a few yards out and Carrick also volleyed wide as the pressure continued.
For all United’s dominance, Fulham should have had a second seven minutes before the interval. Richardson got his toe to Wayne Rooney’s corner and then tore after the breaking Muamer Tankovic.
The young Swede squared to Richardson only for the former United man to lift his shot over from eight yards.
Vidic headed straight at Stekelenburg from a corner but, much like when Rio Ferdinand was embarrassed by Craig Bellamy a few years ago, the Serb, who announced he will be leaving the club in the summer, was brutally exposed for pace by Richardson before Rooney got back to clear the cross.
Stekelenburg was finally pushed into a heroic save when he tipped over from Rooney from close range before Moyes brought on Adnan Januzaj on the hour.
The breakthrough came with 12 minutes remaining when Fulham failed to clear Evra’s cross and van Persie prodded in from Mata’s ball.
A minute later they had a second when Januzaj’s cross was only cleared as far as the edge of the area by Richardson and Carrick’s shot deflected off Scott Parker and flew into the top corner.
Cue an outpouring of emotion inside Old Trafford and there were chances for a third as United felt the war has been won. But after three minutes of added time at the end, Richardson’s shot was saved by De Gea and Bent tapped in Fulham’s equaliser.
Moyes remained typically defiant afterwards and maintained nobody will be looking forward to facing United, who now travel to Arsenal on Wednesday.
But after yet another disappointment it was tempting to feel that one of the few consolations for him is that this kind of result is still a surprise.
MANCHESTER UNITED (4-2-3-1): De Gea 5; Rafael 4 (Valencia 68, 6), Smalling 6, Vidic 5, Evra 7; Carrick 7, Fletcher 6 (Januzaj 62, 6); Mata 5, Rooney 6, Young 7 (Hernandez 69, 6); Van Persie 6.
FULHAM (4-4-1-1): Stekelenburg 7; Riether 8, Burn 8, Heitinga 7, Riise 7; Tunnicliffe 7 (Parker 65, 7), Sidwell 9, Kvist 6 (Cole 81), Richardson 6; Holtby 7; Tankovic 7 (Bent 46, 7).
Referee: Kevin Friend.